Convergence of Numerical Solution for Diffusion Filtering Model Based on Wavelet Transform

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Convergence of Numerical Solution for Diffusion Filtering Model Based on Wavelet Transform

更新时间：2025-07-09

- Convergence of Numerical Solution for Diffusion Filtering Model Based on Wavelet Transform
- Vol. 43, Issue 4, Pages: 121-124(2009)
- 作者机构：
  
  西安交通大学理学院,西安,710049
- 作者简介：
- 基金信息：
- DOI：
  CLC： O241.84
- Online First：10 April 2009，
  
  Published：2009
- 稿件说明：
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Convergence of Numerical Solution for Diffusion Filtering Model Based on Wavelet Transform[J]. 2009, 43(4): 121-124.
DOI：

Convergence of Numerical Solution for Diffusion Filtering Model Based on Wavelet Transform[J]. 2009, 43(4): 121-124. DOI：

摘要

证明了基于小波变换的扩散滤波模型数值解的收敛性.结果表明

如果假定该模型的弱解存在惟一并满足一些正则性假设

则用半隐迭代格式得到的数值解收敛到原方程的弱解.考虑到图像边缘的多尺度效应

该模型用小波变换模代替以往模型中的梯度模

在去噪的同时较好地保持了图像的边缘信息

并克服了经典去噪模型不能有效地除去图像边缘处噪声的弱点.该模型在医学图像处理中展现了良好的性能.

Abstract

Nonlinear diffusion filtering is conducted based on partial differential equations(PDEs)

and the convergence in a class of diffusion model based on wavelets is proved. If the model has an uniquely regular weak solution

the semi-scheme of the model is thus convergent. The magnitude of the gradient is replaced by the magnitude of the wavelet transform in the model for image denoising while edges are preserved

especially

for medical image processing.

关键词

Keywords

references

LIU Feng. Diffusion filtering in image processing based on wavelet transform[J].Science in China(senies F),2006,49(4):494-503.

PERONA P,MALIK J. Scale space and edge detection using anisotropic diffusion[J]. IEEE TPAMI, 1990,12(7):629-639.

CATTE F, LIONS P L,MOREL J M,et al.Image selective smoothing and edge detection by nonlinear diffusion[J]. SIAM J Num, 1992,29(1):182-193.

EVANCE L C. Partial differential equations[M]. Providence, Rhode Island, USA: American Mathematical Society Prov., 1998.

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